This is not always true... and not a good standard policy.
I would like to see proper pressure tests run on the peak pressure of the same load with regular bullets and also with copper, or other type "special" bullets.
If anything is repeated enough times by enough people, it soon will be treated as fact, whether indeed it is a fact, or is just another unproven theory.
Parker Ackley did considerable experimenting along similar lines, using proper lab equipment. His findings of shooting an over size bullet through a barrel was there would be a spike in the pressure, but the spike would come well before peak pressure was reached, thus peak pressure was not increased.
In a centre fire bottle neck cartridge peak pressure is reached when the bullet is several inches down the bore. By this time the over sized, (or solid copper bullet,) is engraved by the rifling and has no greater resistance going through the barrel, then a regular bullet.
Right after WW2 Fred Barnes renewed his bullet making business, which had been halted during war time. The first bullets made after WW2 for a few selected calibres were quite innovative. The jackets were made from copper tubing, the same copper tubing you can buy in a hardware store, he stated. Lead was heat soldered into the core. they were pointed with just a bit of lead exposed in the nose. A brother of mine ordered several hundred from Barnes in each of 150 grain and 200 grain, which we shot in at least two different 30-06 rifles.
The copper jackets were so much thicker and stronger than normal bullet jackets, that as far as I'm concerned, those bullets were nearly identical to the long, modern solid copper bullets. They became a very popular hunting bullet, but of course it didn't hurt that Jack O'Connor was vouching for them!
My brother got an experienced reloader to load them for us and those 200 grain bullets were loaded hot, in relation to any ordinary 200 grain bullet. The primers were even painted red, as a caution not to shoot them in rifles other than those they were designed for. But, we shot them in our ordinary 30-06 rifles and never had any problem with excessive pressure.
I shot moose, mule deer and bear with each weight of bullet and they were very effective.